Showing papers on "Brillouin zone published in 1970"

Superlattice and negative differential conductivity in semiconductors

Abstract: We consider a one-dimensional periodic potential, or "superlattice," in monocrystalline semiconductors formbeyd a periodic variation of alloy composition or of impurity density introduced during epitaxial growth. If the period of a superlattice, of the order of 100A, is shorter than the electron mean free path, a series of narrow allowed and forbidden bands is expected duet o the subdivision of the Brillouin zone into a series of minizones. If the scattering time of electrons meets a threshold condition, the combined effect of the narrow energy band and the narrow wave-vector zone makes it possible for electrons to be excited with moderate electric fields to an energy and momentum beyond an inflection point in the E-k relation; this results ina negative differential conductance in the direction of the superlattice. The study of superlattices and observations of quantum mechanical effects on a new physical scale may provide a valuable area of investigation in the fieId of semiconductors.

Electronic Band Structure and Optical Properties of Graphite from a Variational Approach

Abstract: The electronic band structure of graphite has been calculated from an ab initio variational approach using a linear-combination of atomic-orbitals (LCAO) basis of Bloch states, including nonspherical terms in the one-electron crystal potential. Matrix elements of the Hamiltonian are evaluated directly without any tight-binding approximations. The optical transitions deduced from the energy bands calculated using a single-layer crystal model agree nicely with recent polarized-light reflectance measurements. Details of the band structure are calculated for the three-dimensional Brillouin zone and related to the results obtained using the single-layer crystal structure. The results are encouraging, not only from the standpoint that the method employed is an ab initio approach with no special a priori assumptions, but also because the band structure is quite insensitive to the particulars of the crystal potential function.

On the magnetic excitations in nickel

Abstract: By comparing measured and calculated versions of the generalized magnetic response function of nickel over a wide range of temperatures it is shown that the much-discussed simple model of an itinerant-electron ferromagnet based on a random-phase-approximation treatment of the Hubbard Hamiltonian accounts, in its essentials, for the magnetism of that substance. Thermal neutron inelastic scattering techniques were used to explore the whole Brillouin zone of wave vectors K in nickel up to energies ▄ω of some 2k B T C over the range of temperatures up to 2T C; the computations were based on direct evaluation of the Lindhard expression for the generalized susceptibility, using a tight-binding band structure, followed by exchange enhancement of the spin part as per Izuyama, Kim and Kubo. The contribution to the neutron scattering from orbital motion of the electrons was estimated to be small, and in a special experimental investigation a satisfactorily low upper limit on this quantity for our present p...

Time-Resolved Investigations of Stimulated Brillouin Scattering in Transparent and Absorbing Media: Determination of Phonon Lifetimes

Abstract: Stimulated Brillouin scattering was studied both theoretically and experimentally. The evolution in time of the scattering process, its dependence on frequency, and the influence of optical absorption were analyzed. For quantitative investigations, the individual shapes of the laser and signal pulses were taken into account. Strong transient effects predicted by theory were confirmed experimentally. The amplification of Brillouin light was measured in a generator-amplifier system using single-mode giant laser pulses. Several liquids, glasses, and quartz were investigated. The experimental results allow the determination of phonon lifetimes $\ensuremath{\tau}$ and of elasto-optic constants. In our amplifier system, accurate values of $\ensuremath{\tau}$ are obtained for $\ensuremath{\tau}l3$ nsec, i.e., for liquids and some solids. The limitation of the method is discussed. In absorbing media, stimulated thermal Brillouin scattering was observed in quantitative agreement with theory.

Zwei-Phononen-Absorptionsspektren und Dispersion der Schwingungszweige in Kristallen der Kalkspatstruktur

Abstract: Polarized reflection spectra between 4000 and 20 cm−1 and absorption spectra (at temperatures of liquid helium) between 2000 and 650 cm−1 have been measured of the isomorphous crystals NaN03, CaCO3, MgCO3 (D3d6) and of CaMg (CO3)2 (C3i2) The wavenumbers of the fundamental infrared transitions and of the two-phonon-combinations have been determined The combinationbands show a structure, which allows some insight into the wavevector dispersion of the phonon branches of these crystals Selection rules have been worked out for several points in the interior and on the border of the Brillouin zone By comparison with the spectra they give evidence for the presence of critical points of the phonon-branches for wavevectors parallel to the trigonal axis of the crystal

Inelastic neutron scattering investigation of spin waves and magnetic interactions in α-Fe2O3

Abstract: Spin waves in antiferromagnetic α-Fe2O3 have been studied at temperatures of 240 and 290° K by means of inelastic neutron scattering. We report here the first determination of the acoustical branch throughout the entire Brillouin zone and the first observation of the optical branch. The latter shows little dispersion throughout the zone, and has an energy of 1125° K (97 meV) at the zone centre. At the zone boundaries a gap of 20 to 70° K exists between the two branches. Heisenberg interaction parameters Jm defined through a Hamiltonian were obtained through fitting of the data to theoretical expressions for the dispersion relations. The following values were obtained for the first five nearest neighbours: J1 = 6.0 ± 1.6° K, J2 = 1.6 ± 0.6° K, J3 = −29.7 ± ± 2.0° K, J4 = −23.2 ± 1.0° K and J5 = −1.0 ± 1.0° K. Interactions to farther neighbours were found to be weak. Neutron intensity data were partly invoked in obtaining the interaction parameters, as two sets of parameters could fit the energy data almost equally well, but they predicted different relative intensities for the two branches in certain regions of the reciprocal space. All spin waves of energy larger than 80° K, including the entire optical branch, were found to be unaffected by the Morin spin-flip transition at 261° K temperature. The spin-wave data were used to calculate the sublattice magnetization, the Neel and the Curie-Weiss temperatures, the perpendicular susceptibility at low temperatures and the density of spin-wave state spectrum. [Russian Text Ignored]

Temperature Coefficient of the Refractive Index of Diamond- and Zinc-Blende-Type Semiconductors

Abstract: We have calculated the temperature coefficient of the long-wavelength refractive index of several group-IV and III-V semiconductors, using the Penn model for the electronic contribution to the dielectric constant. The isotropic band gap of this model is identified with the band gap at the $X$ point of the Brillouin zone, which can be simply expressed in terms of pseudopotential coefficients. The explicit temperature dependence of this gap is calculated by applying to these pseudopotential coefficients the appropriate Debye-Waller factors. The thermal expansion effect is obtained in the manner suggested recently by Van Vechten. Good agreement between the calculated and the observed temperature dependence of the long-wavelength refractive index is found.

The Valence Band Structure of Tellurium. I. The k·p Perturbation Method

Abstract: The valance band structure of tellurium near the corner of the Brillouin zone is derived, with the use of the group theory and the k · p perturbation method. The main features of the obtained valence band are the existence of the k z -linear term and of the trigonal warping about the k z axis. Because of the k z -linear term S k z , the uppermost valence band has a double maximum or a single maximum, depending on the ratio of S 2 /4 B | Δ 1 | larger or smaller than one, where Δ 1 and B are the spin-orbit interaction and band parameters, respectively. The present theory is also applicable to selenium.

On the theory of surface states in nearly free electron systems

Abstract: The existence of surface states in band gaps of a nearly free electron band structure is investigated. While in gaps at the Brillouin zone boundary one finds such a state only for positive potential matrix element, there a surface state always exists for band gaps inside the Brillouin zone.

Magnetic and Magneto‐Optical Properties of Some Rare‐Earth and Yttrium Orthochromites

Abstract: From the magnetic susceptibility measurement on YCrO3 above TN=141°K, two exchange constants J1 and J2 are estimated to be J1=−8.7 cm−1 and J2=−1.0 cm−1. In DyCrO3 weak ferromagnetism is observed along the a axis, with TN=146°K. When temperature goes below 5°K, the direction begins to rotate towards the b axis. In SmCrO3 a spin reorientation is found. The direction of weak ferromagnetism changes from the c axis to the a axis when the temperature is lowered below the reorientation temperature Tr=35≈40°K. The magnitude of the weak ferromagnetic moment of Cr3+ decreases rapidly below Tr. Using the values of J1 and J2, we estimate the magnon energies at high‐symmetry points on the Brillouin zone surfaces in YCrO3. By comparing these magnon energies with the optically observed sidebands of the R lines, one may assign the sidebands to the combined excitations of one exciton and one magnon, and of one exciton and two magnons. The observed temperature dependence of these sidebands supports this assignment. The ze...

Lattice Dynamics of Terbium

Abstract: The frequency-wave-vector dispersion relation for the normal modes of vibration of terbium at room temperature has been measured by means of slow-neutron inelastic scattering techniques. The triple-axis spectrometer at the Oak Ridge high flux isotope reactor was used, mostly in the constant-$Q$ mode of operation. Phonon frequencies for wave vectors along the principal symmetry directions have been determined and, in addition, measurements of phonon frequencies along the boundaries of the Brillouin zone and along a more general direction are reported. The data have been fitted with a Born-von K\'arm\'an force model which includes interactions out to the eighth nearest neighbor. The interactions have been assumed to be general (tensor) out to the fourth neighbor and axially symmetric beyond. The model has been used to calculate a frequency distribution function $g(\ensuremath{ u})$ and related quantities such as the lattice specific heat and Debye temperature.

Energy band structure of aluminium by the augmented plane wave method

Abstract: The band structure of metallic aluminium has been calculated by the augmented plane wave method. The energy values and wave functions were computed for the equivalent of 2048 points in the Brillouin zone and for energies ranging from the bottom of the conduction band (3s, 3p) to approximately 0.4 Ry above the Fermi energy. The density of states and the Fermi energy were determined using a variant of an accurate method developed by Gilat and Rauben heimer (Phys. Rev.144 (1966), 390). The results are discussed and compared with earlier results.

The influence of magnetic breakdown on the high field magnetoresistance of aluminium

Abstract: The transverse magnetoresistance, pxx, of an aluminium single crystal has been measured at 4·2°K in fields in the [001] direction up to 60 koe. Above 20 koe it is observed to undergo large oscillations, periodic in reciprocal field, with a frequency of 4·59 × 105 oe. The oscillations are superimposed on a background whose slope increases with field. The Hall component of resistance, pyx, is found to be proportional to field and not to oscillate, and the longitudinal magnetoresistance, pzz, does not saturate and undergoes small oscillations. The cause of the behaviour of pxx and pyx is shown to be magnetic breakdown, which allows holes to change from one orbit to another in an adjacent Brillouin zone using a third zone part of the Fermi surface as a bridge. This mechanism alters the effective paths of the electrons and leads to a higher resistance than would obtain if only simply closed orbits were possible. The resistance oscillations are a consequence of the field dependence of the probability o...

Effect of Single-Ion Anisotropy on Two-Spin-Wave Bound State in a Heisenberg Ferromagnet

Abstract: We consider the scattering of two spin waves in a uniaxial (easy axis) Heisenberg ferromagnet with single-ion anisotropy. The two-spin-deviation problem is solved exactly at zero temperature. We find (for $Sg\frac{1}{2}$), in addition to the usual two-spin-wave bound states, a new "single-ion bound state," in which at the zone corner the two spin deviations are on the same site. When the magnitude of the anisotropy is comparable to the exchange interaction, the single-ion bound state becomes the dominant feature of the bound-state spectrum. For arbitrary spin there is a critical anisotropy strength above which the single-ion bound state exists throughout the Brillouin zone. We conclude that the presence of single-ion anisotropy enhances the possibility of experimental observation of the bound states.

Lattice Vibrations of Cu2O at the Long Wave Limit

Abstract: A study of the lattice dynamics of cuprite at the centre of the Brillouin zone is made and the force constants and the effective charge deduced The energies of the optically inactive phonons are calculated and their symmetry determined The symmetry of the upper valence band of the crystal is identified

Dynamics of the rutile structure. I. Space group representations and the normal mode analysis

Abstract: Multiplier group approach has been used to analyse the normal vibrations of the rutile structure. The irreducible representations at various critical points in the Brillouin zone of the crystal are listed. The basis vectors for the stud of the lattice vibrations have been derived using the projection operator technique and are tabulated. The general form of the atomic displacements at the critical points has been discussed.

Aperture Corrections for Sound‐Absorption Measurements with Light Scattering

Abstract: Even small collection angles in the receiving optics can appreciably broaden, distort, and shift Brillouin lines observed in a light‐scattering experiment, thereby causing errors in both sound absorption and sound velocity. A general expression for the observed lineshape is derived for a Lorentzian scattering line in terms of the distribution of thermal phonons and the shape of the collection aperture. Relaxational effects are also considered. For a square aperture, a closed‐form solution is obtained and discussed. Applicable correction formulas for the true linewidth and lineshift are derived. To first approximation, Brillouin line is the sum of two arctan functions.

Second-order Raman spectrum of ZnSe

Abstract: The first- and second-order Raman spectra of ZnSe have been measured and an interpretation of the spectra has been carried out. The first-order spectrum yielded the values and for the longitudinal and transverse optical phonons at the center of the Brillouin zone. The zone boundary frequencies at the critical points X, L, and W have been estimated from the second-order spectrum. These frequencies were chosen to be consistent with both the experimental results and a theoretical model. The resulting values were further checked for consistency with a sum rule and by using regularities observed previously in the phonon spectra of zinc blende semiconductors.

Phonon Instabilities and Interactions near Solid‐State Phase Transitions

Abstract: The role of phonon instabilities (soft modes) in several types of solid‐state structural phase transitions has recently been demonstrated by inelastic light‐scattering experiments. The symmetry of the soft phonon mode relates the crystal structures above and below Tc, and the temperature dependence of its frequency is associated with various crystal properties near Tc. Examples of both Brillouin zone‐center (q = 0) and zone‐boundary (q≠0) soft modes are presented. The interactions between optic and acoustic phonons respOnsible for sound‐velocity anomalies near Tc are discussed for several classes of phase transitions (ferroelectric, order‐disorder, etc.). While emphasis is placed on phase transitions in crystals of the perovskite structure (e.g., SrTiO3), some attention is also given to interesting transitions in other types of crystals.

Local Pseudopotential Model for GaSb: Electronic and Optical Properties

Abstract: A local-pseudopotential calculation for GaSb using six form factors and one spin-orbit parameter has been found to give good agreement with the known features of the band structure. The reflectivity and wavelength-modulated reflectivity calculated using this band structure are in good agreement with experiment. All prominent features in the optical spectra can be identified with interband transitions in specific regions of the Brillouin zone.

Approximate calculation of electronic band structures. IV. Density of states for transition metals

Abstract: Density-of-states curves for chromium, iron, nickel and copper are calculated using the band-structure scheme of Hubbard and Dalton and the Gilat- Raubenheimer (1966) method. In each case estimates are given for the Fermi energy and the density of states at the Fermi energy. The accuracy of the Gilat-Raubenheimer method is investigated by calculating the density-of-states for copper and iron using varying numbers of k-points in the Brillouin zone. It is concluded that the main features of the density-of-states function are accurately determined with the use of only 200-300 k-points in the 1/48 section of the Brillouin zone.

Hartree-Fock energy bands in LiCl

Abstract: Using local orbital Hartree-Fock orbitals for the Li+ and Cl- ions and the mixed basis method of energy band calculations, the one-electron energy bands of the LiCl crystal were computed for the points Gamma , X and L in the first Brillouin zone. The p-like valence band is found to be 7.84 eV wide and the s-like valence band is found to be 3.03 eV wide. These bands are primarily formed from the outer 3s and 3p halogen states. The band gap at Gamma is computed to be 10.81 eV. At the point X, the s-like state X1 and the d-like state X3 are found to lie lowest and to be essentially degenerate. The use of the Fock exchange is seen to produce significant changes in the band structure when compared with previous calculations using model potentials.